Equation Problems (Perimeter)
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Question 1 of 3
1. Question
Find `x` if the perimeter of the triangle below is `44`cm. `x=` (8)
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Inverse Operations
When moving a term to the other side of an equation, the operation is inversed.First, form an equation knowing that the Perimeter of a shape is the sum of all sides.`P=44`cmSide `1=x` cmSide `2=(x+6)`cmSide `3=(3x2)`cm`P` `=` Side `1` `+`Side `2` `+`Side `3` `44` `=` `x` `+``(x+6)` `+``(3x2)` Substitute the values `44` `=` `5x+4` Simplify `5x+4` `=` `44` To solve for `x`, it needs to be alone on one side.Start by moving `4` to the other side by subtracting `4` from both sides of the equation.`5``x` `+4` `=` `44` `5``x` `+4` `4` `=` `44` `4` `5``x` `=` `40` `44` cancels out Finally, remove `5` by dividing both sides of the equation by `5`.`5``x` `=` `40` `5``x``divide5` `=` `40``divide5` `x` `=` `8` `5divide5` cancels out `x=8` 
Question 2 of 3
2. Question
An isosceles triangle has a perimeter of `55`cm and a base that is `5`cm less than either of the other `2` equal sides. What are the lengths of all three sides?
Equal Side `1=` (20)cmEqual Side `2=` (20)cmBase `=` (15)cm
Hint
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Inverse Operations
When moving a term to the other side of an equation, the operation is inversed.First, label the values and form an equation knowing that the Perimeter of a shape is the sum of all sides.Equal Side `1=x`Equal Side `2=x`Base `=(x5)``P=55`cmEqual Side `1` `+`Equal Side `2` `+`Base `=` `P` `x` `+``x` `+``x5` `=` `55` Substitute the values `3x5` `=` `55` Simplify To solve for `x`, it needs to be alone on one side.Start by moving `5` to the other side by adding `5` to both sides of the equation.`3``x` `5` `=` `55` `3``x` `5` `+5` `=` `55` `+5` `3``x` `=` `60` `5+5` cancels out Finally, remove `3` by dividing both sides of the equation by `3`.`3``x` `=` `60` `3``x``divide3` `=` `60``divide3` `x` `=` `20` `3divide3` cancels out Substitute `x=20` to find each side length.Equal Side `1` `=` `x` `=` `20`cm Equal Side `2` `=` `x` `=` `20`cm Base `=` `x` `5` `=` `20` `5` `=` `15`cm Check our workTo confirm our answer, add the `3` numbers and check if the sum is `55`.`20+20+15` `=` `55` `55` `=` `55` Since the equation is true, the answer is correct.Equal Side `1=20`cmEqual Side `2=20`cmBase `=15`cm 

Question 3 of 3
3. Question
A rectangle is twice as long as it is wide. The total perimeter is `126`cm. What are the dimensions of this rectangle?
Length`=` (42)cmWidth`=` (21) cm
Hint
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Inverse Operations
When moving a term to the other side of an equation, the operation is inversed.First, draw a rectangle and label it using the given statement: “A rectangle is twice as long as it is wide.”This means if the width is `w`, the length should be `2w`Form an equation knowing that the Perimeter of a shape is the sum of all sides.`P=126`cmSide `1` and `2=w` cmSide `3` and `4=2w` cm`P` `=` Side `1` `+`Side `2` `+`Side `3` `+`Side `4` `126` `=` `w` `+``w` `+``2w` `+``2w` Substitute the values `126` `=` `6w` Simplify `6w` `=` `126` Now, to solve for `w`, it needs to be alone on one side.Remove `6` by dividing both sides of the equation by `6`.`6``w` `=` `126` `6``w` `divide6` `=` `126` `divide6` `w` `=` `21` `6divide6` cancels out Finally, substitute `w=21` to the dimensions of the rectangle.Length `=` `2``w` `=` `2(``21``)` `=` `42` cm Width `=` `w` `=` `21` cm Length`=42` cmWidth`=21` cm 
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